"But I think both clubs realise that this matter now needs to be concluded so that we can all move on and prepare for the new season."
Martinez will also take goalkeeping coach Inaki Bergara and masseur Oscar Brau with him to join his new-look backroom team at Wigan but the two were out-of-contract at Swansea.
The 35-year-old hugely-respected manager - whom Celtic approached to replace to Gordon Strachan before the Parkhead turned to West Brom boss Tony Mowbray - is now set for an emotional return to Wigan after an eight year absence.
Martinez alongside fellow Spaniards Jesús Seba and Isidro Díaz joined the then bottom division club as one of Wigan's 'Three Amigos' and spent six seasons in Wigan making 180 appearances for the club.
Latics fans hailed Martinez as Wigan's greatest cult hero in a BBC poll and now he is set to return to the club he left on a free for Motherwell in July 2001.
Martinez also played three-and-half years in two spells at Swansea before the unproven manager was offered the chance to serve his managerial apprenticeship at the Liberty Stadium in February 2007 as Kenny Jackett's replacement.
He quit playing and excelled in his first job as manager and inspired Swansea to the League One championship in his first full season while playing attractive and stylish football.
Martinez continued his beautiful football philosophy in Swansea's first year back in English football's second tier for 24 years as the Welsh club narrowly missed out on a play-off place.
Swansea's trademark total football earned Martinez many plaudits and was particularly highlighted when the Swans beat holders Portsmouth 2-0 at Fratton Park in the fourth round of last season's FA Cup.
Jenkins, who last week admitted the departure of Martinez and his coaching staff had "clearly ripped the heart out of" the club, is now looking for a replacement for Martinez.
Former Wales captain Gary Speed, ex-Watford manager Aidy Boothroyd and Exeter City's back-to-back promotion winning boss Paul Tidsdale have been linked with the Swans job that Martinez helped make so appealing.
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